To solve the problem step-by-step, we need to calculate the probability of two independent events:
1. The probability that the coin will land below the sixth step.
2. The probability that the coin will land heads up.
Step 1: Probability of landing below the sixth step
There are 7 stairs, so the stairs are numbered 1 to 7.
The problem specifies that we are interested in the probability of landing below the sixth step, meaning the coin can land on any of the steps 1 through 5.
- Total number of possible steps = 7
- Favorable outcomes (landing on steps 1 through 5) = 5
So, the probability of landing below the sixth step is:
[tex]\[
\text{Probability}_{\text{below sixth step}} = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{5}{7}
\][/tex]
Step 2: Probability of landing heads up
A fair coin has two possible outcomes: heads or tails. Each outcome has an equal probability.
So, the probability of landing heads up is:
[tex]\[
\text{Probability}_{\text{heads up}} = \frac{1}{2}
\][/tex]
Step 3: Combined probability of both events
Since these two events are independent (the outcome of one does not affect the outcome of the other), we can find the combined probability by multiplying the probabilities of the individual events:
[tex]\[
\text{Combined probability} = \text{Probability}_{\text{below sixth step}} \times \text{Probability}_{\text{heads up}} = \frac{5}{7} \times \frac{1}{2}
\][/tex]
[tex]\[
\text{Combined probability} = \frac{5}{14}
\][/tex]
Now we compare this result with the given choices:
- [tex]\( \frac{1}{7} \)[/tex]
- [tex]\( \frac{1}{14} \)[/tex]
- Not given
- [tex]\( \frac{1}{2} \)[/tex]
Since [tex]\(\frac{5}{14}\)[/tex] isn't one of the provided options, the correct answer is:
C. not given
